The results in Table REF  are to illustrate the performance of finding the learning rate using Gibbs posterior with scaling algorithm in [1]} and [2]}. Since the true MCID is almost certain to be in the range of observed \(X\)  values, the results here for both GPC and SafeBayes are based on uniform prior on \([X_{(1)}, X_{(n)}]\) , the sample range.
Here we observe that the GPC is able to choose the learning rate such that the desired 95% coverage target for each sample size. SafeBayes, on the other hand, tends to choose too large of a learning rate, leading to (sometimes severe) under-coverage.
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